Jack Ma still has the spartan apartment in the Chinese city of Hangzhou where the former English teacher started Alibaba.com in 1999. As the e-commerce company grew, executives and employees often hunkered down there for inspiration while trying to come up with the next big thing.

Big doesn't come close to describing Alibaba Group Holding Ltd. now.

Taobao, a website dreamed up in Mr. Ma's apartment a decade ago, has about 800...